Catadioptric imaging system with dioptric assembly of the petzval type

ABSTRACT

A catadioptric optical imaging system comprises a dioptric assembly (20) and a catoptric assembly (21), which are positioned with respect to each other to form an imaging system of long focal length. The dioptric assembly (20) comprises two confocal paraboloidal mirrors (22, 23) arranged to form a telescope of the Mersenne type. The catoptric assembly (21) comprises lens elements arranged in two groups, viz., a field group (25) and a relay group (26), which are coaxially disposed with respect to the dioptric assembly (20). Only two different optical materials, viz., calcium fluoride crystal and Hoya LAC7 glass, are used in making the lens elements of the dioptric assembly (20). The dioptric assembly (20) is color-corrected at five wavelengths and has only negligible secondary and higher-order spectra in a wavelength band extending from the ultraviolet region to the near infrared region of the optical spectrum.

This application is a division of Ser. No. 676,295 filed on Nov. 29,1984.

TECHNICAL FIELD

This invention relates to optical imaging systems, and more particularlyto optical imaging systems of long focal length.

BACKGROUND OF THE INVENTION

Aberrations inherent in the design of a dioptric or catadioptric systemvary proportionately as the design is scaled up or down, where thescaling factor is the focal length of the system. As the design of adioptric or catadioptric imaging system of given fixed f-number (alsocalled "relative aperture" or "focal ratio") is scaled up to provide alonger focal length for the system, the monochromatic and chromaticaberrations inherent in the design increase concomitantly as the focallength increases.

An optical imaging system having tolerable monochromatic and chromaticaberrations in a specified wavelength band for a given f-number andgiven focal length cannot generally be enlarged in scale to provide alonger focal length for the same f-number, while the same degree ofcorrection for monochromatic and chromatic aberrations is maintained. Anenlargement in the scale of the imaging system to provide a longer focallength for the same f-number would generally cause the aberrationsinherent in the design of the system to increase to such an extent thatre-optimization of the design would become necessary in order to reducethe monochromatic and chromatic aberrations to a tolerable level.

Refractive imaging systems having a relatively high degree of colorcorrection at long focal lengths (i.e., at focal lengths longer than afew meters) could be designed using various combinations of opticalmaterials for bringing two or more wavelengths to a common focus.However, until the method described in co-pending U.S. patentapplication Ser. No. 419,705 for selecting optical materials fordesigning color-corrected optical systems was discovered, very few pairsof optical materials were known that could be used for designingdioptric and catadioptric systems that are color-corrected at more thantwo wavelengths. Furthermore, residual chromatic aberrations (i.e.,secondary and higher-order spectra) inherent in the designs ofrefractive imaging systems are usually intolerable at long focallengths.

SUMMARY OF THE INVENTION

The present invention provides a diffraction-limited catadioptricimaging system of very long focal length.

A catadioptric imaging system according to the present invention iswell-corrected for all aberrations, and has only very small residualcolor error (i.e., secondary and higher-order spectra) in the visibleand near infrared regions of the optical spectrum. Furthermore, animaging system of the present invention has only negligible imagedegradation at focal lengths as long as 100 meters or more.

The catadioptric imaging system of the present invention comprises acatoptric assembly and a dioptric assembly arranged with respect to eachother to form an imaging system of long focal length. The catoptricassembly comprises two confocal paraboloidal reflecting surfaces (viz.,a concave primary mirror having a centrally located aperture, and aconvex secondary mirror positioned so that the foci of the primary andsecondary mirrors coincide), which are arranged to form a telescope ofthe Mersenne type. The two paraboloidal reflecting surfaces areconfigured in accordance with conventional design criteria so that thetelescope is substantially corrected for all aberrations except fieldcurvature. The telescope is afocal so that light gathered by the primarymirror from a distant object is reflected by the secondary mirrorthrough the central aperture on the primary mirror as a non-convergingbeam, which can be considered as a bundle of parallel rays.

The dioptric assembly of the catadioptric imaging system of the presentinvention is located coaxially with respect to the catoptric assembly inthe beam emerging from the central aperture on the primary mirror of thecatoptric assembly, and comprises two groups of lens elements. Eachgroup of lens elements of the dioptric assembly functions separately asan optical relay. The first group of lens elements is designated as thefield group, and the second group of lens elements is designated as therelay group. The entrance pupil for the imaging system is located at theprimary mirror of the catoptric assembly.

The field group and the relay group of the dioptric assembly, when usedin combination with the Mersenne-type catoptric assembly, form atelephoto imaging system that produces diffraction-limited images of adistant object at two spatially separated focal surfaces. The two imagesare conjugate real images having different focal ratios andmagnifications, and each image is well-corrected for the monochromaticaberrations at all visible wavelengths.

A feature of the present invention is that only two different kinds ofoptical materials are use to make the lens elements comprising thedioptric assembly, yet color correction is achieved at five wavelengthswith only negligible residual color error (i.e., secondary andhigher-order spectra at wavelengths between the discrete wavelengths forwhich color correction occurs). The design form of the dioptric assemblyis comparatively simple, requiring only spherical lens surfaces. Thefield group of the dioptric assembly comprises four lens elementspositioned in a Petzval arrangement, and a fifth lens element positionedto function as a field flattener. The relay group of the dioptripassembly comprises four lens elements arranged in the manner of amicroscope objective. The field group provides a first image of thedistant objectat the first focal surface, and the relay group provides amagnified image of the first at the second focal surface.

The design form for an optical imaging system according to the presentinvention can be scaled up to a focal length greater than 100 meters,while maintaining diffraction-limited performance and a stable variationof image centroid with respect to wavelength throughout the visible andnear infrared regions of the spectrum for narrow field applications.

DESCRIPTION OF THE DRAWING

FIG. 1A is a schematic profile drawing of an optical imaging system ofthe present invention comprising an afocal telescope of the Mersennetype and a dioptric assembly having lens elements made of only twodifferent kinds of optical materials, where four possible positions A,B, C and D for the dioptric assembly relative to the telescope areindicated.

FIG. 1B is a schematic profile drawing of a portion of an alternativeembodiment of an optical imaging system of the present invention,wherein a beam splitter is positioned between the field group and thefirst focal plane of the system shown in FIG. 1A in order to change thedirection of the optic axis of the system.

FIG. 2, which comprises FIGS. 2A and 2B drawn on separate sheets tofacilitate their perusal in juxtaposition, is an enlarged profiledrawing of the optical imaging systems of FIG. 1A with the dioptricassembly located at position A.

FIG. 3 is a plot of paraxial marginal ray height versus wavelength atthe second focal plane of the imaging system of FIG. 1A for a focallength of 100 meters, where the dioptric assembly is located at positionA.

FIG. 4 is a plot of change in back focal distance versus wavelength atthe second focal plane of the imaging system of FIG. 1A for a focallength of 100 meters, where the dioptric assembly is located at positionA.

FIG. 5 is a plot of change in paraxial principal ray height versuswavelength at the second focal plane of the imaging system of FIG. 1Afor a focal length of 100 meters, where the dioptric assembly is locatedat position A.

FIG. 6 is a plot of marginal ray height versus wavelength at the secondfocal plane of the imaging system of FIG. 1A for a focal length of 100meters, where the dioptric assembly is located at position A.

FIG. 7 is a plot of marginal ray height versus wavelength at the firstfocal plane of the imaging system of FIG. 1A for a focal length of 100meters, where the dioptric assembly is located at position A.

FIG. 8 is a plot of image centroid variation versus wavelength at thesecond focal plane of the imaging system of FIG. 1A for a focal lengthof 100 meters, where the dioptric assembly is located at position A.

FIG. 9 is a plot of image centroid variation versus wavelength at thesecond focal plane of the imaging system of FIG. 1A for a focal lengthof 100 meters, where the dioptric assembly is located at position B.

FIG. 10 is a plot of image centroid variation versus wavelength at thesecond focal plane of the imaging system of FIG. 1A for a focal lengthof 100 meters, where the dioptric assembly is located at position C.

FIG. 11 is a plot of image centroid variation versus wavelength at thesecond focal plane of the imaging system of FIG. 1A for a focal lengthof 100 meters, where the dioptric assembly is located at position D.

BEST MODE OF CARRYING OUT THE INVENTION

In FIG. 1A, a long-focus catadioptric imaging system comprising adioptric assembly 20 and a catoptric assembly 21 is illustrated inschematic profile. The catoptric assembly 21 is configured as atwo-mirror afocal telescope of the Mersenne type in which a concaveparaboloidal pirmary mirror 22 and a convex paraboloidal secondarymirror 23 are positioned in fixed disposition with respect to each otherso that the reflecting surfaces of the mirrors 22 and 23 face each otherwith the foci of the two reflecting surfaces coinciding. A discussion oftelescopes of the Mersenne type is found in The History of the Telescopeby Henry C. King, Sky Publishing Corporation, Cambridge, Mass. (1955),pages 48-49.

The imaging system of the present invention as shown in FIG. 1A isrotationally symmetric about a line through the centers of curvature ofthe reflecting surfaces of the two mirrors 22 and 23, which line definesthe optic axis of the system. The entrance pupil of the system islocated at the primary mirror 22, which is the larger of the two mirrors22 and 23. A circular hole 24 is provided at the apex of the primarymirror 22 centered on the optic axis of the system. Light from a distantobject (which for convenience is considered as an infinitely distantobject) is gathered by the primary mirror 22 and is reflected to thesecondary mirror 23, from which the light is reflected through the hole24 in the primary mirror 22 as a non-converging beam along the opticaxis of the system.

In accordance with ray tracing convention, the light emitted by (orreflected from) the infinitely distant object is represented in FIG. 1Aby parallel rays directed from left to right. However, as far as theutility of the imaging system of the present invention is concerned,there is no requirement that the oject be located infinitely far awayfrom the light-gathering primary mirror 22. An object located at afinite distance from the reflecting surface of the primary mirror 22could be focussed by appropriately adjusting the separation between theprimary mirror 22 and the secondary mirror 23 along the optic axis.

The dioptric assembly 20, as described in detail hereinafter, functionsin conjunction with the catoptric assembly 21 as an imaging and relayapparatus that is well-corrected with respect to both chromatic andmonochromatic aberrations. However, in accordance with presentinvention, the dioptric assembly 20 could be used alone as an opticalimaging and relay apparatus. The utility of the dioptric assembly 20 isnot limited to use in combination with a telescope.

The dioptric assembly 20 comprises lens elements arranged in two groups25 and 26, which are disposed coaxially with respect to the catoptricassembly 21 along the optic axis of the system, and which arerotationally symmetric with respect to the optic axis of the system.Each of the groups 25 and 26 of lens elements functions independently ofthe other as an optical relay. For the purspose of describing theinvention as illustrated in FIGS. 1A, 1B, 2A and 2B, the first group 25is designated as the field group, and the second group 26 is designatedas the relay group.

Only two different optical materials are used in making the various lenselements comprising the dioptric assembly 20. In accordance with thepresent invention, these two different optical materials, which are usedin fabricating the lens elements in each of the two groups 25 and 26,are selected so that the dioptric assembly 20 is color-corrected at fivewavelengths in the visible and near infrared regions of the opticalspectrum, and has only negligible residual color error (i.e., secondaryand higher-order spectra) at the intervening wavelengths between thefive wavelengths for which color correction is achieved.

A method of selecting a pair of optical materials for fabricating thelens elements of a refractive optical system so as to provide colorcorrection at five wavelengths was described in co-pending U.S. patentapplication Ser. No. 419,705, which is incorporated herein by reference.Among the color-corrected optical systems described in patentapplication Ser. No. 419,705 was a collimator, whose lens elements aremade from a pair of optical materials consisting of calcium fluoride(CaF₂) crystal and Hoya LAC7 glass, which provides color correction atfive wavelengths with practically negligible residual color error in thevisible and near infrared regions of the spectrum.

In setting out to design a refractive optical imaging system for anapplication requiring color correction at five wavelengths with onlynegligible residual color error at the intervening wavelengths, anoptical designer with knowledge of the disclosure in patent applicationSer. No. 419,705 would realize that the pair of optical materialsconsisting of calcium fluoride crystal and Hoya LAC7 glass could be usedfor designing such a system. However, having selected this pair ofoptical materials, the designer would then have to apply his skill indeveloping a design form for the system in which the monochromaticaberrations as well as the chromatic aberrations are corrected tosatisfy the image quality requirements of the system.

The dioptric assembly 20, as illustrated in FIG. 1A and as shown ingreater detail in the enlarged view obtained by juxtaposing FIGS. 2A and2B, comprises some lens elements made of calcium fluoride crystal andother lens elements made of Hoya LAC7 glass. Disks (and other shapes) ofcalcium fluoride crystal ready for grinding and polishing to opticalspecifications are commercially available from suppliers such as HarshawChemical Company of Solon, Ohio and Optovac, Inc., of North Brookfield,Mass. Likewise, disks (and other shapes) of Hoya LAC7 glass ready forgrinding and polishing to optical specifications are marketed by HoyaCorporation of Tokyo, Japan. The Hoya catalog number "LAC7" isuniversally understood by optical designers as unambiguously identifyingthe particular optical glass so specified.

With reference to FIG. 1A, the field group 25 of the dioptric assembly20 forms a first image of the distant object on a first focal surface27, and the relay group 26 forms a magnified second image on a secondfocal surface 28 of the first image appearing on the first focal surface27. The images formed on the first and second focal surfaces 27 and 28are conjugate images of the distant object at different f-numbers anddifferent magnifications. The f-number (also called the "relativeaperture" or "focal ratio") of an optical system is defined as the ratioof the equivalent focal length f of the system to the diameter of theentrance pupil for the system. For the imaging system shown in FIG. 1A,the subsystem comprising the catoptric assembly 21 and the field group25 of lens elements located to the left of the first focal surface 27has an f-number of 7.5, which is conventionally written as f/7.5. Theimaging system as a whole (i.e., the catoptric assembly 21 and theentire dioptric assembly 20 to the left of the second focal surface 28)has an f-number of 80, which is written as f/80. The first and secondfocal surfaces 27 and 28 are substantially planar surfaces.

In FIG. 1A, four different positions A, B, C and D are indicated for thedioptric assembly 20 with respect to the catoptric assembly 21. Thepositions A, B, C and D are four particular positions for the dioptricassembly 20 from among a continuum of possible positions along the opticaxis of the system. The relative locations of the individual lenselements comprising the dioptric assembly 20 remain unchanged withrespect to each other, regardless of how the position of the dioptricassembly 20 as a whole may be changed with respect to the catoptricassembly 21.

For any given position of the dioptric assembly 20 relative to thecatoptric assembly 21, the design form of the imaging system illustratedin FIG. 1A could be scaled up or down depending upon the operationalrequrirements of the system. For a given scale, the locations of thefirst and second focal surfaces 27 and 28 remain constant relative tothe positions of the individual lens elements of the groups 25 and 26comprising the dioptric assembly 20, regardless of the position of thedioptric assembly 20 relative to the catoptric assembly 21. A devicesuch as a photographic plate or a charge-coupled device (CCD) could beplaced at the second focal surface 28 for detecting the image producedby the system.

For applications in which it is necessary or desirable that theconjugate images formed at the two focal surfaces 27 and 28 be detectedsimultaneously, it is necessary that a detector be placed at the firstfocal surface 27 without obstructing the beam that must pass through therelay group 26 to the second focal surface 28. A modification of theimaging system of the present invention, as illustrated in FIG. 1B,enables the conjugate images formed at the focal surfaces 27 and 28 tobe detected simultaneously by positioning a beam splitter 37 on theoptic axis of the system between the field group 25 and the focalsurface 27.

The beam splitter 37 transmits a first portion of the beam along theoriginal direction of the optic axis to a focal surface 27', which islocated precisely where the first focal surface 27 would be located inthe absence of the beam splitter 37. A detector located at the focalsurface 27' detects the image formed by the field group 25 withoutobstructing the beam passing through the relay group 26 to the secondfocal surface 28, because the beam splitter 37 in effect changes thedirection of the optic axis as far as the relay group 26 is concerned.

The beam splitter 37 reflects a second portion of the beam away from theoriginal direction of the optic axis at an angle determined by theorientation of the reflecting surface of the beam splitter 37 withrespect to the original direction of the optic axis. As shown in FIG.1B, the beam splitter 37 "folds" the optic axis of the imaging systemaway from its original direction, and the first focal surface 27 isaccordingly moved to a new location on the "folded" optic axis. There isnot detector at the first focal surface 27 to obstruct the beam passingto the relay group 26. The relay group 26 is located on the folded opticaxis, and the magnified second image formed on the second focal surface28 of the first image appearing on the first focal surface 27 isdetected by a detector located at the second focal surface 28. The twofocal surfaces 27 and 28 are both located away from the originaldirection of the optic axis, and hence are unobstructed by the detectorat the focal surface 27'.

A compensation plate 38 is positioned between the field group 25 and thefocal surface 27' (preferably between the beam splitter 37 and theposition 27') along the original direction of the optic axis of thesystem. The compensation plate 38 is substantially transparent to thefirst portion of the beam transmitted by the beam splitter 37, andcompensates for aberrations introduced by the beam splitter 37. Since nodetector is located at the first focal surface 27 on the folded opticaxis to obstruct the second portion of the beam transmitted by the fieldgroup 25, the detector placed at the second focal surface 28 can detectthe image formed at the second focal surface 28, while the detectorplaced at the focal surface 27' on the original direction of the opticaxis can simultaneously detect the image formed at the first focalsurface 27.

As shown in detail in FIG. 2A, the field group 25 comprises four lenselements 31, 32, 33 and 34 positioned in a Petzval-type arrangement, anda fifth lens element 35 positioned between the lens element 34 and thefirst focal surface 27 to function as a field flattener (i.e., tocorrect the image formed at the first focal surface 27 for fieldcurvature). As shown by juxtaposing FIGS. 2A and 2B so that the lineA--A in FIG. 2A coincides with the line A--A in FIG. 2B, the lenselements 31, 32, 33 and 34 are positioned in the beam passing throughthe aperture 24 so as to bring the beam to a focus at the first focalsurface 27. The lens elements 31 and 32 in combination have a netpositive dioptric power, and the lens elements 33 and 34 in combinationlikewise have a net positive dioptric power. Together, the lens elementsof the field group 25 provide an image at the first focal plane 27 thatis color-corrected at five wavelengths over the visible and nearinfrared spectral band. As shown in detail in FIG. 2B, the relay group26 comprises four lens elements 41, 42, 43 and 44 arranged in the mannerof a microscope objective to magnify the image appearing at the firstfocal surface 27, and to focus the magnitude image at the second focalsurface 28.

The optical prescription of the catadioptric imaging system of thepresent invention whose dioptric assembly 20 is located at position A,as shown in FIG. 1A, is specified in Table I below in terms of theequivalent focal length f of the entire catadioptric system as follows:

                  TABLE I                                                         ______________________________________                                        OPTICAL PRESCRIPTION FOR CATADIOPTRIC                                         IMAGING SYSTEM WITH TWO FOCAL SURFACES                                        Surface                                  Mate-                                No.    Radius    Thickness  N.sub.e                                                                              V.sub.e                                                                             rial                                 ______________________________________                                         1     -.037500 f                                                                              -.017580 f [Primary Mirror]                                   2     -.002343 f                                                                              .017580 f  [Secondary                                                                    Mirror]                                            3     ∞   .026385 f  [Hole]     Air                                     4      .004060 f                                                                              .000141 f  1.43500                                                                              95.06 CaF.sub.2                             5     -.004514 f                                                                              .000023 f               Air                                   6     -.004340 f                                                                              .000078 f  1.65426                                                                              58.15 LAC7                                  7     -.054611 f                                                                              .006008 f               Air                                   8      .001270 f                                                                              .000125 f  1.43500                                                                              95.06 CaF.sub.2                             9     -.002708 f                                                                              .000024 f               Air                                  10     -.005043 f                                                                              .000070 f  1.65426                                                                              58.15 LAC7                                 11      .005345 f                                                                              .001230 f               Air                                  12     -.000604 f                                                                              .000047 f  1.65426                                                                              58.15 LAC7                                 13     -.000727 f                                                                              .001615 f               Air                                  14     ∞   .000359 f  [lst Focal Plane]                                                                        Air                                    15      .000306 f                                                                              .000031 f  1.65426                                                                              58.15 LAC7                                 16      .000249 f                                                                              .000092 f               Air                                  17      .000206 f                                                                              .000039 f  1.43500                                                                              95.06 CaF2                                 18     -.000519 f                                                                              .000010 f               Air                                  19      .000884 f                                                                              .000030 f  1.65426                                                                              58.15 LAC7                                 20      .000139 f                                                                              .000011 f               Air                                  21      .000158 f                                                                              .000039 f  1.43500                                                                              95.06 CaF.sub.2                            22     -.000555 f                        Air                                  23     ∞              [2nd Focal Plane]                                 ______________________________________                                    

where the concave paraboloidal reflecting surface of the primary mirror22 is indicated as surface No. 1, the convex paraboloidal reflectingsurface of the secondary mirror 23 is indicated as surface No. 2, thehole 24 is indicated as a dummy or imaginary surface No. 3, the surfacesof the lens elements of the field group 25 are numbered consecutivelyfrom No. 4 to No. 13, the first focal surface 27 is indicated as surfaceNo. 14, the surfaces of the lens elements of the relay group 26 arenumbered consecutively from No. 15 to No. 22, and the second focalsurface 28 is indicated as surface No. 23, in accordance withconventional practice, from left to right along the optic axis of thesystem.

The "radius" listed in the second column of Table I for each surface isan indicated multiple of the focal length f of the entire catadioptricsystem, with a positive or negative sign according to whether theparticular surface is convex or concave. The mirror surfaces areparaboloidal, and the "radius" for each mirror surface is actually theradius of a sphere that osculates the vertex of the paraboloidalsurface. The curvatures of a paraboloidal surface and its osculatingsphere are practically the same over a substantial area about the vertexof the paraboloidal surface. The lens surfaces are all spherical, andthe "radius" for each lens surface is the radius of curvature of thespherical surface expressed as a multiple of the focal length f of thecatadioptric system.

The "thickness" of each lens element and the separation between opposingsurfaces on adjacent lens elements are measured along the optic axis ofthe catadioptric imaging system, and are likewise expressed in Table Ias multiples of the focal length f of the entire catadioptric system.The value for thickness (or separation) listed in the third column ofthe table for each surface refers to the thickness of the lens element(or the spacing between adjacent surfaces) to the right of the indicatedsurface.

The symbol N_(e) in the heading of the fourth column of Table Irepresents the refractive index of the material from which theparticular lens element is made as measured at the wavelength of themercury e line, i.e., λ₀ =0.54607 micron.

The symbol V₃ in the heading of the fifth column of Table I representsthe Abbe number of the material from which the particular lens elementis made. The Abbe number is defined as the ratio ##EQU1## where N_(F),is the refractive indesx at the cadmium F' line (i.e., 0.47999 micron)and N_(C') is the refractive index at the cadmium C' line (i.e., 0.64385micron). The values of the refractive index and the Abbe number listedin the fourth and fifth columns of the table for each lens surfacerefere to the lens element to the right of the indicated surface.

Each positive lens element of the dioptric assembly 20 is made ofcalcium fluoride (CaF₂) crystal, and each negative lens element is madeof Hoya LAC7 glass as indicated in the right-hand column of the table.The material from which each lens element is made technically specifiedin terms of the index of refraction N₃ and the Abbe number V_(e).However, as a practical matter, optical designers ordinarily specify thematerial of each lens element in a refractive optical system in terms ofthe chemical composition (in the case of a crystal) or themanufacturer's name and catalog number (in the case of an opticalglass).

The catadioptric imaging system as specified by the optical prescriptionin Table I includes several subsystems, each of which is useful in itsown right independently of its use as a subsystem in the catadioptricimaging system. Thus, with reference to Table I, the subsystemcomprising the optical components from surface No. 4 through surface No.14 form a lens system of the Petzval type, which is independently usefulas a dioptric infinite conjugate imaging system that is color-correctedfor five wavelengths. The optical prescription for this Petzval lenssystem, by itself, is specified in Table II below in terms of theequivalent focal length f of the Petzval lens system (i.e., the fieldgroup 25 in FIG. 1A).

                  TABLE II                                                        ______________________________________                                        OPTICAL PRESCRIPTION FOR PETZVAL LENS SYSTEM                                  Surface No.                                                                            Radius   Thickness N.sub.e                                                                             V.sub.e                                                                             Material                              ______________________________________                                         4        0.6930 f                                                                              0.0240 f  1.43500                                                                             95.06 CaF.sub.2                              5       -0.7706 f                                                                              0.0039 f              Air                                    6       -0.7409 f                                                                              0.0133 f  1.65426                                                                             58.15 LAC7                                   7       -9.3223 f                                                                              1.0255 f              Air                                    8        0.2167 f                                                                              0.0213 f  1.43500                                                                             95.06 CaF.sub.2                              9       -0.4622 f                                                                              0.0041 f              Air                                   10       -0.8608 f                                                                              0.0120 f  1.65426                                                                             58.15 LAC7                                  11        0.9124 f                                                                              0.2100 f              Air                                   12       -0.1031 f                                                                              0.0080 f  1.65426                                                                             58.15 LAC7                                  13       -0.1241 f                      Air                                   14       ∞            [Focal Plane]                                     ______________________________________                                    

where the radii and the thicknesses are expressed as multiples of thefocal length f of the Petzval lens system. It is noted that the "f" ofTable II is different from the "f" of Table I. In Table I, f is thefocal length of the entire catadioptric imaging system as shown in FIG.1A, with the dioptric assembly 20 located at position A. In Table II, onthe other hand, f refers to the focal length of the field group 25considered as an independent Petzval lens system.

Also, with reference to Table I, the subsystem comprising the opticalcomponents from surface No. 15 through surface No. 23 form a finiteconjugate imaging system, which is independently useful as, e.g., amicroscope objective,. The optical prescription for this finiteconjugate imaging system, by itself, is specified in Table III below interms of its equivalent focal length f (i.e., the focal length of therelay group 26 in FIG. 1A).

                  TABLE III                                                       ______________________________________                                        OPTICAL PRESCRIPTION FOR FINITE CONJUGATE                                     IMAGING SYSTEM                                                                Surface                                                                       No.    Radius     Thickness N.sub.e                                                                             V.sub.e                                                                             Material                              ______________________________________                                        15     0.6720 f   0.0684 f  1.65426                                                                             58.15 LAC7                                  16     0.5468 f   0.2014 f              Air                                   17     0.4522 f   0.0855 f  1.43500                                                                             95.06 CaF.sub.2                             18     -1.1377 f  0.0212 f              Air                                   19     1.9364 f   0.0684 f  1.65426                                                                             58.15 LAC7                                  20     0.3054 f   0.0252 f              Air                                   21     0.3467 f   0.0855 f  1.43500                                                                             95.06 CaF.sub.2                             22     -1.2162 f                        Air                                   23     ∞              [Image Plane]                                     ______________________________________                                    

where the radii and the thicknesses are expressed as multiples of thefocal lengh f of the finite conjugate imaging system.

Further, with reference to Table I, the subsystem comprising the opticalcomponents from surface No. 4 through surface No. 23 form a diotricinfinite conjugate imaging system that is color-corrected at fivewavelengths. The optical prescription for the dioptric infiniteconjugate imaging system is specified in Table IV below in terms of itsequivalent focal length f (i.e., the focal length of the dioptricassembly 20 in FIG. 1A).

                  TABLE IV                                                        ______________________________________                                        OPTICAL PRESCRIPTION FOR DIOPTRIC INFINITE                                    CONJUGATE IMAGING SYSTEM WITH TWO FOCAL                                       SURFACES                                                                      Surface                                  Mate-                                No.    Radius     Thickness N.sub.e                                                                              V.sub.e                                                                             rial                                 ______________________________________                                         4     0.0648 f   0.00224 f 1.43500                                                                              95.06 CaF.sub.2                             5     -0.0720 f  0.00037 f              Air                                   6     -0.0692 f  0.00125 f 1.65426                                                                              58.15 LAC7                                  7     -0.8712 f  0.09584 f              Air                                   8     0.0203 f   0.00200 f 1.43500                                                                              95.06 CaF.sub.2                             9     -0.0432 f  0.00038 f              Air -10 -0.0805 f  0.00112                                                    f 1.65426 58.15 LAC7                 11     0.0853 f   0.01963 f              Air                                  12     -0.0096 f  0.00075 f 1.65426                                                                              58.15 LAC7                                 13     -0.0116 f  0.02577 f              Air                                  14     ∞    0.00573 f [1st Focal Plane]                                                                        Air                                    15     0.0049 f   0.00050 f 1.65426                                                                              58.15 LAC7                                 16     0.0040 f   0.00147 f              Air                                  17     0.0033 f   0.00062 f 1.43500                                                                              95.06 CaF.sub.2                            18     -0.0083 f  0.00016 f              Air                                  19     0.0141 f   0.00050 f 1.65426                                                                              58.15 LAC7                                 20     0.0022 f   0.00018 f              Air                                  21     0.0025 f   0.00062 f 1.43500                                                                              95.06 CaF.sub.2                            22     -0.0089 f                         Air                                  23     ∞              [2nd Focal Plane]                                 ______________________________________                                    

where the radii and the thicknesses are expressed as multiples of thefocal length f of the dioptric infinite conjugate imaging system.

In addition, with reference to Table I, the subsystem comprising theoptical components from surface No. 1 through surface No. 14 form acatadioptric imaging system, which is color-corrected five wavelengths.The optical prescription for this catadioptric imaging system isspecified in Table V below in terms of its equivalent focal length f(i.e., the focal length of the system comprising only the catoptricassembly 21 and the field group 25 in FIG. 1A).

                  TABLE V                                                         ______________________________________                                        OPTICAL PRESCRIPTION FOR CATADIOPTRIC IMAGING -SYSTEM WITH SINGLE FOCAL       SURFACE                                                                       Surface                                  Mate-                                No.    Radius    Thickness  N.sub.e                                                                              V.sub.e                                                                             rial                                 ______________________________________                                        1      -0.4000 f -0.18750 f [Primary Mirror]                                  2      -0.0250 f 0.18750 f  [Secondary                                                                    Mirror]                                           3      ∞   0.28145 f  [Hole]       Air                                  4       0.0433 f 0.00150 f  1.43500                                                                              95.06 CaF.sub.2                            5      -0.0482 f 0.00024 f               Air                                  6      -0.0463 f 0.00083 f  1.65426                                                                              58.15 LAC7                                 7      -0.5825 f 0.06409 f               Air                                  8       0.0135 f 0.00133 f  1.43500                                                                              95.06 CaF.sub.2                            9      -0.0289 f 0.00026 f               Air                                  10     -0.0538 f 0.00075 f  1.65426                                                                              58.15 LAC7                                 11      0.0570 f 0.01313 f               Air                                  12     -0.0064 f 0.00050 f  1.65426                                                                              58.15 LAC7                                 13     -0.0078 f                         Air                                  14     ∞              [Focal Plane]                                     ______________________________________                                    

where the radii and the thicknesses are expressed as multiples of thefocal lenth f of the catadioptric imaging system comprising thecataoptric assembly 21 (i.e., the telescope) and the field group 25(i.e., the Petzval lens system) as shown in FIG. 1A.

The number of wavelengths for which color correction is achieved, andthe extend of the residual chromatic aberration (i.e., secondary andhigher-order spectra) for the image formed at the second focal surface28 of the imaging system of the present invention when the dioptricassembly 20 is located at position A in FIG. 1A, are indicated by the"wavelength scan" curves of FIGS. 3-6. Similarly, the number ofwavelengths for which color correction is achieved, and the extent ofthe residual chromatic aberration for the image formed at the firstfocal surface 27, are indicated by the "wavelength scan" curve of FIG.7.

The concept of color correction of refractive optical system forparticular specified wavelengths refers to the fact that the paraxialmarginal ray height of the system is precisely zero for the specifiedwavelengths, whereby paraxial rays of the specified wavelengths arebrought to a common focus on the optic axis of the system. The conceptof reduction in secondary and higher-order spectra, on the other hand,refers to a reduction of residual chromatic errors at wavelengthsbetween the particular wavelengths for which color correction isachieved.

It has been found that the "wavelength scan" curves of FIGS. 3-7 do notvary appreciably as the location of the dioptric assembly 20 relative tothe catoptric assembly 21 is changed from position A to any otherposition (as represented by the particular positions B, C and D in FIG.1A) along the optic axis of the imaging system. In a particularapplication, the position of the dioptric assembly 20 along the axis ofthe imaging system could be selected to accommodate the positioning ofother optical components such as beam splitters, beam-steering mirrorsor optical filters in the space between the catoptric assembly 21 andthe dioptric assembly 20.

In FIG. 3, a plot of paraxial marginal ray height (conventionallydesignated "PY") versus wavelength at the second focal surface 28 isshown for the catadioptric imaging system of the present invention,where the dioptric assembly 20 is located at position A in FIG. 1A. Aparaxial marginal ray passing through an optical system is a ray thatoriginates at an object point on the optic axis of the system and passesthrough the system in the immediate vicinity of the optic axis. When theobject point is infinitely distant from the entrance pupil of thesystem, a paraxial marginal ray for a particular wavelength enters thesystem parallel to the optic axis and is refracted by the components ofthe system to form an image at a paraxial focal surface of the systemfor that wavelength. The point of intersection of the paraxial mrginalray for the given wavelength with the optic axis of the system definesthe paraxial focal point of the system for that wavelength. A surfaceperpendicular to the optic axis and passing through the paraxial focalpoint for the given wavelength defines the paraxial focal surface of thesystem for that wavelength. The location of the paraxial focal point(and therefore the location of the paraxial focal surface) generallyvaries with wavelength; and this variation is called the chromaticvariation of focus, or the axial chromatic aberration, or thelongitudinal chromatic aberration.

In general, a paraxial marginal ray from an infinitely distant objectpoint intersects the paraxial focal surface of an optical system for aparticular wavelength at a point that is spatially separated from thepoint of intersection of the optic axis of the system with thatparaxialfocal surface. The lateral distance defining the separationbetween the point of intersection of a paraxial marginal ray with asurface and the point of intersection of that surface with the opticaxis of the system is called the paraxial marginal ray "height" of thesystem at that surface.

In general, the value of the paraxial marginal ray height at a givenfocal surface of an imaging system changes with wavelength due to axialchromatic aberration. A point object cannot generally be imaged as apoint (even using only monochromatic light), but instead is imaged as ablur due to monochromatic aberrations and diffraction effects. Ifpolychromatic light (or a continuous spectrum of white light) is used,the resulting image blur has a component due to monochromaticaberrations and a component due to chromatic aberrations, even whendiffraction effects are ignored.

The value of the paraxial marginal ray height at a given focal surfacefor an imaging system at any particular wavelength (e.g., the value of"PY" in the wavelength scan curve of FIG. 3 for the imaging system ofthe present invention) is a measure of the extent of tbe geometricalimage blur (i.e., the image blur without consideration of diffractioneffects) inherent in the system at that particular wavelength. Thevariation of paraxial marginal ray height with wavelength at a givenfocal surface provides an indication of the extent to which axialchromatic aberration is corrected in the system. The wavelength scancurve of FIG. 3 indicates that the imaging system of the presentinvention is color-corrected at five wavelengths in the visible and nearinfrared region of the spectrum as indicated by the five crossings ofthe horizontal axis.

The wavelength scan curve of FIG. 3 is close to the horizontal axis,indicating that paraxial marginal ray height is small, throughout thespectral band from 0.39 micron to 0.8 micron. The ordinate of the curverepresenting paraxial marginal ray height versus wavelength at a givenfocal surface is a measure of the radius of the geometrical blur forthat particular wavelength at that focal surface. For an optical systemthat is color-corrected at only two wavelengths, the wavelength scancurve for paraxial marginal ray height would cross the horizontalb axisat only two points corresponding to the two wavelengths for which colorcorrection has been achieved. The maximum "height" of the wavelengthscan curve for a particular wavelength above or below the horizontalaxis between two crossing points is a measure of the maximum radius ofthe geometrical image blur for that wavelength at the focal surface, andis what is meant by the "secondary spectrum" for that wavelengthinterval.

For an optical system that is color-corrected at three wavelengths, thewavelength scan curve for paraxial marginal ray height would cross thehorizontal axis at three points. The maximum "height" of the wavelengthscan curve in a wavelength band of interest is a measure of the maximumradius of the geometrical image blur, and indicates the tertiaryspectrum of the system. The maximum height of the wavelength scan curvein FIG. 3, which pertains specifically to the diffraction-limitedimaging system of the present invention, indicates negligiblehigher-order spectra throughout the spectral band from about 0.39 micronto about 0.80 micron.

In FIG. 4, a plot of change in back focal distance versus wavelength atthe second focal surface 28 is shown for the catadioptric imaging systemof the present invention, where the dioptric assembly 20 is located atposition A in FIG. 1A. The back focal distance of an imaging system fora particular wavelength is defined as the distance along the optic axisof the system between the focal surface for that particular wavelengthand the refractive surface closes to that focal surface. For acolor-corrected imaging system, paraxial marginal rays at thewavelengths for which color correction has been achieved are brought toa focus at a common focal surface. The back focal distance for thosewavelengths for which color correction has been achieved can beconsidered as a "baseline" back focal distance. Thus, for the imagingsystem of FIG. 1, for which the relay group 26 is shown in greaterdetail in FIG. 28, the "baseline" back focal distance is the distancealong the optic axis between the lens element 44 and the second focalsurface 28.

For the wavelengths at which color correction has not been achieved(i.e., for the wavelengths between the crossing points on the horizontalaxis for the wavelength scan curve of FIG. 3), the paraxial marginalrays are focussed at other focal surfaces whose positions along theoptic axis of the imaging system are dependent upon wavelength. Thechange in back focal distance from the "baseline" back focal distance isshown in FIG. 4 as a function of wavelength. The wavelength scan curveof FIG. 4 provides an indication of the chromatic variation in focalposition along the optic axis of the system, and hence is commonlycalled "longitudinal" or "axial" chromatic aberration.

It is apparent from FIG. 4 that the position of the second focal surface28 does not change appreciably as a function of wavelength over thespectral band from about 0.39 micron to about 0.80 micron. Thus, thepositioning of an instrument to detect the second image formed on thesecond focal surface 28 can remain constant for an imaging systemaccording to the present invention for all wavelengths throughout thevisible and near infrared regions of the spectrum.

In FIG. 5, a plot of change in paraxial principal ray height(conventionally designated "PcY") versus wavelengths at the second focalsurface 28 is shown for the catadioptric imaging system of the presentinvention, where the dioptric assembly 20 is located at position A inFIG. 1A. A paraxial principal ray passing through an optical system is aparaxial ray that originates at an extremity of an extended object andpasses through the center of the entrance pupil of the system. Aparaxial principal ray (also called a chief ray) for a particularwavelength intersects a focal surface of the system at a point that isspatially separated from the point of intersection of the optic axiswith the focal surface. The lateral distance from the optic axis of thesystem to the point of intersection of the paraxial principal ray with asurface is called the paraxial principal ray "height" for that surface.If that surface is a focal surface, the paraxial principal ray heightPcY at that surface corresponds to the geometrical image for thatwavelength.

The value of the paraxial principal ray height at a given focal surfacefor an imaging system changes with wavelength. For a color-correctedimaging system according to the present invention, the paraxialprincipal ray height at the focal surface for which color-correction hasbeen achieved can be considered as a "baseline" paraxial principal rayheight. In FIG. 5, the change in the value of the paraxial principal rayheight from the "baseline" paraxial principal ray height at the secondfocal surface 28 is plotted as a function of wavelength. This change inparaxial principal ray height with wavelength at a focal surfaceprovides a measure of the chromatic variation of image height, which iscommonly called the chromatic difference of magnification, or lateralchromatic aberration, or "lateral color". It is apparent from FIG. 5that the chromatic difference of magnification at the second focalsurface 28 does not change appreciably with wavelength in the spectralband from about 0.39 micron to about 0.80 micron for the imaging systemof the present invention.

In FIG. 6, a plot of marginal ray height (conventionally designated "Y")versus wavelength at the second focal surface 28 is shown for thecatadioptric imaging system of the present invention, where the dioptricassembly 20 is located at position A in FIG. 1A. A marginal ray passingthrough an optical system is a ray that originates at an axial objectpoint and grazes the periphery of the entrance pupil of the system so asto define the maximum cone of rays from that object point that can beaccepted by the system. For an infinitely distant object, the marginalray is parallel to the optic axis with a ray height from the optic axisequal to the radius of the entrance pupil of the system.

The parameters (i.e., ray heights and slopes) of a marginal ray passingthrough an optical system can be calculated by application of Snell'sLaw. As with a paraxial marginal ray, so also a marginal ray intersectsa focal surface of the system at a point that generally is spatiallyseparated from the point of intersection of the optic axis with thefocal surface. The lateral separation between the optic axis of thesystem and the point of intersection of the marginal ray with a surfaceis designated as the marginal ray "height" for that surface. The valueof the marginal ray height at a given focal surface changes withwavelengths due to spherical aberration and the chromatic variation ofspherical aberration (i.e., spherochromatism) inherent in the system.The value of the marginal ray height for a particular wavelength is ameasure of the extent of geometric image blur at that particularwavelength taking spherical aberration into consideration.

it is instructive to compare the wavelength scan curve for marginal rayheight as shown in FIG. 6 with the wavelength scan curve for paraxialmarginal ray height as shown in FIG. 3. The curve in FIG. 6, which wasgenerated by actual ray tracing according to Snell's Law, shows fivecrossings of the horizontal axis. The flatness of the curve in FIG. 6shows that spherochromatism and residual chromatic aberrations arenegligible throughout the visible region of the spectrum. It is apparentfrom the curves of FIGS. 3 and 6 that an imaging system according to thepresent invention not only provides coincidence of paraxial focus (i.e.,paraxial color correction) at five wavelengths, but also providescoincidence of marginal focus (i.e., marginal color correction) at fivewavelengths.

In FIG. 7, a plot of marginal ray height versus wavelength at the firstfocal surface 27 is shwon for the catadioptric imaging system of thepresent invention, where the dioptric assembly 20 located at position Ain FIG. 1A. The wavelength scan curve of FIG. 7 indicates that thesubsystem comprising the catoptric assembly 21 and the Petzval-typefield group 25 at f/7.5 provides coincidence of marginal focus at fivewavelengths, and also has practically negligible higher-order spectraand is well-corrected for spherochromatism throughout the spectral bandfrom about 0.39 micron to 0.8 micron.

Wavelength scan curves for paraxial marginal ray height, change in backfocal distance, change in paraxial principal ray height, and marginalray height at the second focal surface 28, and wavelength scan curvesfor marginal ray height at the first focal surface 27 as in FIG. 7, whenplotted for the dioptric assembly 20 located at each of the positions B,C and D indicated in FIG. 1A, are substantially identical to thecorresponding wavelength scan curves shown in FIGS. 3, 4, 5, 6 and 7.Thus, the various wavelength scans are substantially invariant withrespect to the position of the dioptric assembly 20 relative to theposition of the catoptric assembly 21. Therefore, a long-focus imagingsystem having the design form shown in FIG. 1A can be used in a varietyof different configurations requiring various dispositions of thedioptric assembly 20 relative to the catoptric assembly 21 withoutsubstantially changing the imaging capabilities of the system.

An imaging system according to the present invention could be used in aninstrument for precisely tracking a distant object. In general, theposition of the centroid of the image of a distant object at the focalsurface of an imaging system changes with the wavelength of the opticalradiation emitted by (or used to illuminate) the object. In FIG. 8, thevariation of the position of the image centroid of a distant object onthe second focal surface 28 is shwon as a funtion of a wavelength forthe imaging system of the present invention having a focal length of 100meters, where the dioptric assembly 20 is located at position A in FIG.1A.

The curve of FIG. 8 indicates the fidelity of an imaging systemaccording to the present invention in preserving the centroid locationof the image of a distant object over the entire visible spectrum. Thus,a tracking instrument embodying an imaging system of the presentinvention enables image centroiding within microradian accuracy to beachieved for a plurality of different narrow wavelength bands within thevisible spectrum.

In FIGS. 9, 10 and 11, the variation of the position of the imagecentroid of a distant object on the second focal surface 28 for theimaging system of the present invention is shown as a function ofwavelength for a focal length of 100 meters, where the dioptric assembly20 is located at positions B, C and D, respectively, in FIG. 1A. Acomparison of the wavelength scan curves of FIGS. 8, 9, 10 and 11indicates that the variation of image centroid position with respect towavelength for an optical imaging system according to the presentinvention changes, but only to a minor extent, with change in theposition of the dioptric assembly 20 relative to the catoptric assembly21. In general, the variation of the position of the image centroidprovided by a tracking instrument using an imaging system according tothe present invention diminishes as the spacing between the dioptricassembly 20 and the catoptric assembly 21 decreases.

This invention has been described above in terms of a particularlong-focus refractive imaging system designed with particular focalratios and magnifications using particular optical materials that arecommercially available at the present time. However, other long-focusrefractive imaging systems with different focal ratios andmagnifications, which are designed according to the teachings of theforegoing disclosure and accompanying drawing, would likewise be withinthe scope of the invention. The embodiments of the invention describedherein are to be considered as illustrative of the invention, which isdefined more generally by the following claims and their equivalents.

I claim:
 1. A catadioptric imaging system comprising a catoptricassembly and a dioptric assembly, said catoptric assembly comprising aprimary mirror for gathering light from a distant object and a secondarymirror for reflecting the gathered light as a nonconverging beam alongan optic axis of the system, said dioptric assembly comprising a lenssystem of the Petzval type positioned on said optic axis, said lenssystem consisting of a plurality of lens elements of only two differentkinds of optical materials, said plurality of lens elements coactingwith each other so as to bring paraxial marginal rays passing throughsaid lens system to a common focus at five wavelengths, said lens systemthereby being color-corrected at exactly five wavelengths.
 2. Thecatadioptric imaging system of claim 1 wherein said optical materialscomprise calcium fluoride crystal and a glass having a refractive indexof approximately 1.65 and an Abbe number of approximately 58.15 at awavelength of 0.546 micron.
 3. The catadioptric imaging system of claim2 wherein said glass is Hoya LAC7 glass.
 4. The catadioptric imagingsystem of claim 1 wherein said lens system comprises a first lenselement, a second lens element, a third lens element, a fourth lenselement and a fifth lens element, said first, second, third, fourth andfifth lens elements being consecutively disposed along said optic axis,said first lens element being made of calcium fluoride crystal, saidsecond lens element being made of Hoya LAC7 glass, said third lenselement being made of calcium fluoride crystal, said fourth lens elementbeing made of Hoya LAC7 glass, and said fifth lens element being made ofHoya LAC7 glass.
 5. The catadioptric imaging system of claim 4 whereinsaid first lens element has a surface with a positive radius ofcurvature of approximately 0.0433 times the focal length of the systemand a surface with a negative radius of curvature of approximately0.0482 times the focal length of the system, said second lens elementhas a surface with a negative radius of curvature of approximately0.0463 times the focal length of the system and a surface with anegative radius of curvature of approximately 0.5825 times the focallength of the system, said third lens element has a surface with apositive radius of curvature of approximately 0.0135 times the focallength of the system and a surface with a negative radius of curvatureof approximately 0.0289 times the focal length of the system, saidfourth lens element has a surface with a negative radius of curvature ofapproximately 0.0538 times te focal length of the system and a surfacewith a positive radius of curvature of approximately 0.0570 times thefocal length of the system, and said fifth lens element has a surfacewith a negative radius of curvature of approximately 0.0064 times thefocal length of the system and a surface with a negative radius ofcurvature of approximately 0.0078 times the focal length of the system,said first lens element having a thickness along said optic axis ofapproximately 0.00150 times the focal length of the system, said secondlens element being separated from said first lens element along saidoptic axis by approximately 0.00024 times the focal length of thesystem, said second lens element having a thickness along said opticaxis of approximately 0.00083 times the focal length of the system, saidthird lens element being separated from said second lens element alongsaid optic axis by approximately 0.06409 times the focal length of thesystem, said third lens element having a thickness along said optic axisof approximately 0.00133 times the focal length of the system, saidfourth lens element being separated from said third lens element alongsaid optic axis by approximately 0.00026 times the focal length of thesystem, said fourth lens element having a thickness along said opticaxis of approximately 0.0075 times the focal length of the system, saidfifth lens element being separated from said fourth lens element alongsaid optic axis by approximately 0.01313 times the focal length of thesystem, said fifth lens element having a thickness along said optic axisof approximately 0.00050 times the focal length of the system.